Research On The The Reliability Methods For The Aleatory And Epistemic Uncertaint Structures

In engineering practice, there are various uncertainties in the material properties,geometric parameter and loading of structure systems. In order to improve the outputperformances of the structures under uncertain circumstances, some new methods foruncertainty propagation and reliability sensitivity analysis are investigated in thispaper. The detailed contents are listed as follows:1. Based on detailed research about local domain Monte Carlo simulation, theshortcomings of this method are discussed and reformed. Through introducing the βsphere to local domain Monte Carlo simulation to reduce the computational effort ofthe limit state function in the safe domain, an advanced local domain Monte Carlosimulation is proposed in this paper to improve the calculation efficiency of thefailure probability.2. The local and global sensitivity analysis models are established for thestructures under non-probabilistic uncertain environment to provide morecomprehensive information for the designer. The local sensitivity analysis is used toreflect the sensitivity of the non-probabilistic reliability index with respect to theparameters of the interval variables, whiles the global sensitivity analysis reflects theaverage effect of the entire range of input variables on the shape and position of thenon-probabilistic reliability index. The high-efficient solutions are also proposed forthe two sensitivity analysis models.3. For the structure with aleatory and epistemic uncertainties, throughpartitioning the input variables space of into mutually exclusive focal element whichcontains the interval variables and random variables, a new approach is established todeal with the mixture of both types of uncertainties. The belief measure and theplausibility measure are used to measure the security of the uncertain structures. Afterobtaining the belief and plausibility function, the designer can identify the effect ofthe two types of uncertainties on the output response of the structure and collect moreinformation for the most critical input uncertain variables.4. The structure involving input random variables with uncertainty distributionparameters and input non-random variables is investigated in this paper. Theuncertainties of the distribution parameters of the random variables and inputnon-random variables are all described by the interval models. The unified reliability analysis model for this hybrid uncertainty is established by separating the distributionparameters and variability uncertainties of the random variables according to equalprobability transformation method. Based on the kriging surrogate model method, ahigh-efficient solution is proposed to solve the proposed unified hybrid uncertaintymodel.5. To analyze the effects of specific regions of the aleatory and epistemicuncertain variables on the failure probability, a regional sensitivity analysis (RSA)technique called contribution to failure probability (CFP) plot is developed in thispaper. This RSA technique can detect the important aleatory and epistemic uncertainvariables, and also measure the contribution of specific regions of these importantinput variables to the failure probability. The properties of the RSA technique aregiven and the feasibility of it for engineering practice is also tested. According to theRSA results, the engineer can achieve a targeted reduction of the failure probability bytrimming the range of the aleatory and epistemic uncertain variables.6. By reasonably introducing probability transition model with a standarduniform distribution into the membership level of the fuzzy input variable, thereliability models are established under single fuzzy variable and mixed fuzzy-randomvariable, respectively, from the probability perspective. The relation between thetraditional fuzzy reliability model and the proposed fuzzy reliability model, where themembership levels of the different fuzzy input variables take the same standarduniform distribution, is rigorously verified in theory. Meanwhile, the rationality andenvelope of the proposed fuzzy reliability model are revealed when the membershiplevels of the different fuzzy input variables are transformed into the random variableswith independent and standard uniform distribution. The proposed models can minemore useful information and reflect the essence of the fuzzy uncertainty.7. For the uncertain structure with only fuzzy variables, the importance measureindex of the fuzzy variables on the failure probability is proposed in this paper. Thisimportance measure index can reflect the average effect of the membership level ofthe fuzzy variables on the failure probability. Through the relationship of themoment-independent importance measure of the failure probability and thevariance-based importance measure of the corresponding failure domain indicatorfunction, the estimation method for the proposed importance measure index isestablished based on the state dependent parameters (SDP) approach.